Problem: Simplify the following expression: $p = \dfrac{6q^2 - 90q + 300}{q - 5} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $6$ , so we can rewrite the expression: $ p =\dfrac{6(q^2 - 15q + 50)}{q - 5} $ Then we factor the remaining polynomial: $q^2 {-15}q + {50} $ ${-5} {-10} = {-15}$ ${-5} \times {-10} = {50}$ $ (q {-5}) (q {-10}) $ This gives us a factored expression: $\dfrac{6(q {-5}) (q {-10})}{q - 5}$ We can divide the numerator and denominator by $(q + 5)$ on condition that $q \neq 5$ Therefore $p = 6(q - 10); q \neq 5$